To add to the absolute mindfuck that today has been, he has now messaged us as if everything is completely normal: "Totally blown away by the thought and care selecting our pressies. So touched xx" along with about 15 photos of them posing with the presents we gave them. I feel a bit sick even writing that. None of us have responded, obviously.
Again - I'm going to suggest you re-frame this.
Instead of "this is a mindfuck" (it IS, no denying that, but bear with me ...)
try "Ah. He didn't get the drama he wanted from GiftGate, so now he is goading us to try & provoke us into a response".
I'm going to be really annoying and drip-feed now, but in my defence I mainly wrote this because I was doubting whether the hurt and upset was justified or not and didn't want to turn it into a family history essay.
You are justified, of course. But do you want to carry on feeling hurt every time he dreams up a little scheme to hurt you with, or do you want to find a way to let it bounce off you?
Anyone who has a mindfucker in the family KNOWS this isn't about the presents. So don't feel you have to justify that sense of ... hurt, dismay, "oh no not again" "why" "how can I make him stop doing this" & all the rest of the feckin' merry-go-round. BUT! instead - think about the best way to step off the merry-go-round.
I get it - it's not about the presents, it's about how unfair it is that your dad isn't a better, more consistently caring dad, & that goes back decades.
I think (hope?) he might be unwell. In hindsight, I shouldn't be surprised by this as he does have form for being petty and vindictive when he feels slighted, but he can also be kind and supportive and practical and loving. To me, that does suggest it's a mental health thing, as it's not consistent behaviour and him and his sister used to be very close - they live on opposite sides of the country but would meet up for Christmas and birthdays and special events.
He's not unwell.
He's just a mindfucker who isn't above mindfucking his nearest & dearest.
Mindfuckery is more important to him than you & everybody else's feelings.
Also - google "cycle of abuse" & stop hoping that the kind & supportive side of him is the "real" him, & the petty & vindictive side is something you can fix.
Because it isn't.
You can't fix character - this is just who he is. All of it.
All you can do is stick around for the nice side, & Grey Rock -
www.healthline.com/health/grey-rock
OR (in the moment only, so as an ad hoc response, NOT an appeal to him to stop doing it!) walk away each time he does it, telling him why he is no longer welcome to your company when he does XYZ
You need to accept that this is who he is, & stop turning yourself inside out looking for 'reasons' why he acts up. I understand why you are still doing this, because it's more comfortable to have a 'reason' to blame, than blaming dad directly for the hurt he causes.
But all that digging for 'reasons' will give you is more of the same - you trapped on the merry-go-round, spending FAR too much of your life dedicated to giving dad too much of your time, even in the freedom of your own head.
See how he's made you spend so much time already, thinking about him instead of cracking on with your happy life?
I should have spoken up when he told us about the presents.
Why?
You're not his keeper.
If he wants to make a prat of himself, acting out with stupid behaviours designed to make everyone else unhappy enough to ensure he gets to be Star Of The Shit Show - let him.
He doesn't react well to confrontation, which is why we didn't,
Oh, I think he reacts brilliantly to confrontation.
I think he thrives on it, & knows that he's better at it than all of the rest of you combined.
That's why he KEEPS ON INVITING IT.
and I stupidly assumed he was giving rubbish presents alongside good ones - like an actual funny joke.
You weren't stupid.
He told you in advance for a reason - it's so when you all get het up about it, he can blame you for your reaction, instead of owning that he did a shitty thing. You can just already imagine his smugness at being 'confronted' can't you? -
"But I TOLD you I was doing joke presents this year. Can't you take a joke? It's really mean of you not to laugh. It IS funny, you didn't tell me not to so obviously you were in on it, so it's all your own fault."
"You greedy little shits, you're just pissed off because you are venal, I did it to teach you a lesson, I've paid for you all my life, nothing I ever do is good enough for you, you won't even laugh at my joke why am I cursed with such ungrateful brats" etc
In other words - he set you up for a good DARVO'ing - www.banyantherapy.com/darvo/
We sent her and her family our own separate presents (fucking great presents!) which they really appreciated, and we'll call her in a few days to see what she thinks is going on.
DON'T.
See analysis merry-go-round, above.
Of course you can mention it - but stop burdening yourself with the responsibility of investigating, apologising for, mitigating, or otherwise sorting out how any other adult chooses to respond to dad's shitty behaviour.
Your attitude need only be - "meh, that's dad for you. Never mind, at least the rest of us don't pull stupid stunts like that,. I'm not rewarding him with any attention for it, suggest you don't either. Anyway ..." [subject change & move on].
The books are fucking horrible though. For those who might be wondering - Book 1: The End of Loneliness - about three siblings who become estranged after their parents die. Funnily enough, we are three siblings and our lovely mum died 3 years ago. Book 2: A Little Life. I spent a month with a crisis team as a teenager being treated for SH and debilitating anxiety and struggled for years with it, he used to drive me to appointments. 
Which is how you know he's not "unwell" - he's a headfucker.
Fuck him, & fuck his arsehole ideas of fun.
For now, we're going to pretend this hasn't happened. No comments, no acknowledgement, no reaction and LC for the foreseeable. I like all the petty revenge ideas and am quite tempted to ship everything back to him, but I don't want to give him the satisfaction and I'm not sure I'll get an honest conversation out of him.
Excellent.
Just watch that "for now".
You will get NO joy out of any attempt to stop him behaving like some kind of Cluster-B Dark Triad personality disordered twat. Likely because he IS a ... yeah, you get it.
Do you know about the But We Took You To Stately Homes threads on MN? - if not, search some up, you will find like minds & support there.
You might also find this site a source of relief & understanding - outofthefog.website/toolbox-intro - have a look around it, but focus on how the knowledge helps YOU distance yourself from dad's more unfortunate behaviours - NOT at how to 'fix' them.
Above all - stop acting the peacekeeper.
If GiftGate has hurt other family members, that is NOT of your making, & you don't have to apologise for it, soothe it, find solutions to it, or do anything other than just briefly commiserate, empathise, advise everyone to Grey Rock it, subject change, & move on.